Should I model eyelids?
I guess you have 2 main approaches:


The eyelids are parts of the face mesh. As Hikariztw said you'll animate them with bones or shapekeys. Not easy to do but for a realistic character it's the only solution.





The eyelids are part of the head object but they are separate meshes. You'll rig them to bones and make them go up and down, or rotate, or even just appear and disappear (move outside/inside the head mesh). It's not a realistic solution, so it's good for a cartoon character, and it will be much easier to animate.